Veggies are great for gluten free side dishes, particularly if you cook them simply. Stick with simple toppings - cheese (not pre-grated, because pre grated cheese can have gluten in its non stick coating), oil, vinegar, lemon juice, salt, pepper, herbs and spices.
I'd try to avoid packaged processed foods, because as others have said, gluten shows up everywhere, and often under weird names - soy contains gluten, pre grated cheese often does, even chicken stock often contains gluten.
A garden salad is always good, if you make your own vinaigrette.
Blanch trimmed green beans for a few minutes. Dress with olive oil, fresh lemon juice, salt and pepper, serve warm or at room temperature.
Roasted cauliflower with cumin, or tossed with freshly grated parmesan.
Roasted asparagus spears with olive oil, salt and pepper, shaved parmesan and red pepper flakes.
Sautee corn kernels in a bit of olive oil until they start to brown. Add a handful chopped chives, a bit of crushed garlic, and powdered cumin, and cook for a few more minutes. Turn of the heat and season with salt and lime juice.
Roasted corn salsa - roast the corn in a pan as above, until lightly browned. Cool, toss with chopped cilantro, finely chopped onion, salt and lime juice.
Baked squash wedges with butter, salt and pepper.
Slowly roast halved tomatoes along with the ham.